Ion–Electron Coupling Enables Ionic Thermoelectric Material with New Operation Mode and High Energy Density

Highlights An ion–electron coupled thermoelectric material was successfully prepared, which theoretically proved the ion–electron thermoelectric synergy effect and this material can work for a long time, which promoted low-grade thermal energy conversion. In the new operating mode of ion–electron thermoelectric synergy effect, our ionic thermoelectrics have a high Seebeck coefficient of 32.7 mV K−1 and a high energy density of 553.9 J m−2, enabling self-power for electronic components. Supplementary Information The online version contains supplementary material available at 10.1007/s40820-023-01077-7.


S1 Model for Ion-electron Thermoelectric Synergistic Effect
In this section, we derive the synergistic contribution of the ionic thermodiffusion and electron drift.
The ionic flux and internal energy flux in the electrolyte system can be described by the Onsager relationship [S1, S2]: Where i is the ion species, , ̃, and are the ionic flux, electrochemical potential, and the heat flux across the sample, respectively. , , , are the transport coefficients and is the temperature.
According Han et al., in an electrolyte where both anion and cation valence states are ±1, the thermopower can be expressed as [S2]: Where S is the thermopower, D is the diffusion coefficient, e is the elementary charge. ̂ is Eastman entropy of transfer.
Assuming that both ions and electrons exist in a homogeneous conductive gel, when no potential difference exists, the distribution of ions and electrons should be uniform so that there is no electric field exists (as shown in Fig. 1a.). When a temperature difference is applied across this gel (as shown in Fig. S1), however, ions will diffuse from the hot side to the cold side (known as the Soret effect) resulting in an ionic diffusion current (expressed as JDiff) and a potential difference. At the same time, an electric field (E, purple arrow) is formed inside the conductive gel to balance the ionic diffusion and thus form a drift current (expressed as JDrift). The current generated by the intrinsic Seebeck effect of the conductive gel is denoted by Je-TE.
The general expression of ionic current density can be expressed as [S3]: Where D is the diffusion coefficient, Φ is the potential, μ is the mobility, q is the charge, C is the ion concentration, and z is the ion charge.
The diffusion current can be shown as [S4-S6]: Re-expressing the above equation to account for anions and cations: The drift current generated within the conductive gel can be expressed as: Where σ is the electrical conductivity of the gel, E is the electric field strength.
The current generated by the conductive gel due to the Seebeck effect can be expressed as: Under open circuit conditions, the net current is zero, then we have: Generally, the current generated by the Seebeck effect of the electronic conductor is very small and the Je-TE current contribution can be ignored. So that Eq. (S11) can be simplified as: Then we have: When we define macroscopically, it can be written as: And then, According to the Soret effect of ion diffusion under a temperature difference, the current density generated by the mobile ions can be written as [S7]: Where DT is thermodiffusion coefficient.
Under equilibrium conditions [S7]: In the case of equal charge numbers of anions and cations: Therefore, we can obtain an expression for the Seebeck coefficient under the cooperative work of ion -electrons: Note that: We can conclude that the voltage under ion-electron cooperation is positively correlated with the Soret effect (Eq. S20) and negatively correlated with the conductivity of the gel (Eq. S21).

Fig. S1
Model analysis of ion-electron thermoelectric system. Schematic diagram of particle motion in an ion-electron conductor after applying a temperature difference

Fig. S4
The output voltage curve of CPP900 under a thermal gradient ramp; the thermopower is obtained by dividing the potential difference by the temperature difference. The results show that the thermopower of CPP900 is 12.5 V K -1 , which is a typical performance of e-TE diagram and b result of the thermopower test, with the cold side swapped below and the hot side on top. c Schematic diagram and d result of the thermopower test, with the hot side swapped below and the cold side on top. The test results after changing the direction of the temperature difference are equivalent to the original thermopower. Note that the temperature difference is +20 K, and the voltage is also positive, which proves the consistency between the temperature difference and the thermovoltage. The voltage test curve at a temperature difference of 20 K when only DI water is introduced, indicating that voltage generation is not dependent on water content and/or evaporation. Because previous studies have shown that in some porous carbon structures, the evaporation of water may also cause a potential difference, so it is necessary to exclude the possibility of the potential difference caused by the evaporation of water [S4, S8]. The initial rise in voltage may be caused by the evaporation of water or the movement of a small number of ions (such as H + on the carboxyl group) inside the CPP. As the moisture is depleted, the voltage eventually plateaus to a plateau value, which is the intrinsic thermoelectric effect of the CPP900  The thermal voltage of CPP900-BMIM:Cl apparently lags behind the temperature difference ( Fig.  S11) because the electrical conductivity has a decreasing process during the test. The conductivity of electronic conductors is initially higher than the ionic conductivity (Fig. S12a). This means that the thermoelectric potential generated by the ions can be quickly balanced out by the electrons in the drift electric field. Therefore, for a short period of time after the temperature difference is applied, the potential difference is only a few millivolts (Fig. S12b). With thermal diffusion of ions and dissipation of electrons in the drift electric field, the resistance of the entire device increases (Fig. S12c), exhibiting a decrease in electrical conductivity. A drop in electrical conductivity can lead to a rise in thermovoltage, which can be explained by our theoretical IETS models. Firstly, since the net current is 0, the magnitude of the drift and diffusion currents are equal as seen in the expression below: Nano-Micro Letters S12/S23 Then according to the expression for the drift current: Therefore, when the electrical conductivity ( − ) decreases, the thermovoltage (dV) rises in the case where the ions continue to diffuse.
When the electrical conductivity drops to be comparable with the ionic conductivity, there is an unstable increase in voltage. When the conductivity of the electronic conductor decreases further, the ability of electrons to balance the thermoelectric potential of the ions gradually weakens, resulting in a large increase in the thermoelectric potential of the ions. The thermopower of the electron/ion hybrid system is determined by the charge carrier with higher conductivity, this is consistent with the previous study by Crispin et al [S9].
Therefore, we can reasonably model the change in electrical conductivity and the rise in thermovoltage. Thus, thermovoltage rise can be divided into three stages (Fig. S12d). In stage I, the electrical conductivity is higher than the ionic conductivity. Electrons quickly balance the potential difference created by the ions, and the voltage is expressed as a few millivolts. In stage II, the electrical conductivity gradually drops to be comparable to the ionic conductivity. The ionic thermoelectric potential begins to grow erratically. In stage III, the electrical conductivity drops further. The ability of electrons to balance the potential difference of the ions is minimized, and the electrons cannot quickly balance the potential difference generated by the ions, which is manifested as a rise in voltage      Supplementary Video S1 i-TE cells drive thermo-hygrometer continuously at ΔT = 20 K